12 Difficult Python Questions You Might Take Days To Solve

1) Largest Puddle

You are given a 2D list of integers.

map = [
    [5, 5, 5, 5, 5, 2, 2],
    [5, 4, 3, 3, 5, 2, 2],
    [5, 3, 5, 3, 5, 2, 2],
    [5, 5, 5, 5, 5, 5, 2],
    [5, 5, 5, 5, 2, 1, 5],
    [5, 3, 2, 5, 1, 4, 5],
    [5, 5, 2, 5, 5, 3, 5]
]

Each number represents the height of the land. When it rains, water flows from larger numbers to smaller numbers (horizontally/vertically). Puddles collect when water cannot flow out of the map. Assume that water that flows outside of the map will not form a puddle.

The red area is a puddle as water cannot flow out
The blue area is NOT a puddle, as water can flow out
The green area is a puddle as water cannot flow out
The yellow area is NOT a puddle as water can flow out
The pink area is also NOT a puddle as water can flow out

Our task here would be to write a function largest_puddle(map) that takes in a 2D list map, and returns the coordinates of the largest puddle on the map. For the above map:

{(1,1), (2,1), (1,2), (1,3), (2,3)}

^ the coordinates of the red puddle

2) Finding Island Coordinates

You are given a 2D list of integers (either 0 or 1)

map = [
    [1,1,0,1,1],
    [1,1,0,0,0],
    [0,0,0,0,0],
    [1,1,1,0,0],
]

1’s are land, while 0’s are sea. 1’s that are next to each other (horizontal + vertical only) make up an island. Here, we have 3 islands:

Write a function get_islands(map) that takes in a 2D list map, and returns a list of sets, each set representing 1 island.

[
    {(0, 1), (1, 0), (0, 0), (1, 1)},  # the top-left island
    {(0, 3), (0, 4)},                  # the top-right island
    {(3, 0), (3, 2), (3, 1)}           # the bottom-right island
]

3) Longest Word Chain

You are given a list of English words:

words = ["apple", "orange", "tank", "elephant", "kitten"]

A word chain is a list of English words where the last letter of each word is equal to the first letter of the next word. For instance:

["apple", "elephant"] is a valid word chain
["tank", "kitten"] is a valid word chain
["elephant", "apple"] is not a valid word chain as "apple" does not begin with "t"
["apple", "kitten"] is not a valid word chain as "kitten" does not begin with "e"

Write a function longest_word_chain(words) that takes in a list of English words words, and returns the longest possible valid word chain. For the example above, the longest possible valid word chain is:

["apple", "elephant", "tank", "kitten"]

Or:

["orange", "elephant", "tank", "kitten"]

4) Hollow Diamond

Write a function hollow_diamond(string) that takes in a string string, and prints the following pattern:

hollow_diamond('abcdefgh')

  a
 b h
c   g
 d f
  e

If there are insufficient characters to form a perfect hollow diamond shape, append your string with * characters.

hollow_diamond('abcdefghij')

   a
  b *
 c   *
d     j
 e   i
  f h
   g

Another example:

hollow_diamond('abcdefghijklmnop')

    a
   b p
  c   o
 d     n
e       m
 f     l
  g   k
   h j
    i

Yet another example:

hollow_diamond('abcdefghijklmn')

    a
   b *
  c   *
 d     n
e       m
 f     l
  g   k
   h j
    i

5) Upslope Coordinates

lis = [1, 3, 4, 6, 2, 3, 5, 3, 3, 8, 9]

You are given a list of numbers representing land height. Write a function upslope(lis) that takes in this list of numbers, and returns a 2D list containing sections that are upslope (increasing).

x = upslope(lis)

# [[1, 3, 4, 6], [2, 3, 5], [3, 8, 9]]

6) Contains 1 (No Strings Allowed)

Write a function contains1(n) that takes in an integer n, and returns True if n contains the digit 1, and False otherwise. You cannot use any strings or string methods. (if you could, it’s way too easy)

contains1(21)    # True
contains1(201)   # True
contains1(617)   # True

contains1(22)    # False
contains1(202)   # False
contains1(627)   # False

7) Minimum number of coins

Write a function min_coins(coins, value) that takes in a list coins and an integer value, and returns a dictionary representing the minimum total number of coins we need to make up value. For instance:

min_coins([1, 2, 5], 101)

We have an infinite number of $1 coins, $2 coins and $5 coins
We need to find the minimum number of coins to make $101
In this case, the best possible answer is 20 $5 coins and 1 $1 coin
The function hence returns {1:1, 5:20}

min_coins([2, 3], 20)

We have an infinite number of $2 and $3 coins
We need the minimum number of coins to make up $20
The answer is 6 $3 coins and 1 $2 coin.
The function hence returns {2:1, 3:6}

min_coins([2, 4, 6], 5)

We have an infinite number of $2, $4 and $6 coins to make $5
This is not possible, so we simply return {}

8) Dictionary Parsing

string = '{"apple":4, "orange":5, "pear":6}'

You are given a string representing a Python dictionary. Write a function parse(string) that takes in this string, parses it, and returns the actual dictionary. Assume that keys and values will either be numbers or string, and that there are no nested lists/dicts etc.

Note — You cannot use libraries or the eval or exec function

parse(string)

# {"apple":4, "orange":5, "pear":6}

9) Magic Square

A magic square is a 3x3 grid containing numbers 1 to 9 (each number should appear ONCE). Every 3 consecutive numbers (row, column or diagonal) must add up to 15. An example:

[  [2, 7, 6],
   [9, 5, 1],
   [4, 3, 8]  ]

You are given an incomplete magic square.

magic_square = [
  [2, 0, 0],
  [0, 0, 0],
  [0, 3, 8]
]

Here, 0 means you need to fill it in. Write a function solve(magic_square) that takes in the incomplete magic square, fills it in with the correct numbers, and returns the complete magic square.

def solve(magic_square):
    # stuff

solve(magic_square)
# [  [2, 7, 6],
#    [9, 5, 1],
#    [4, 3, 8]  ]

10) Square root

Write a function sqrt(n) that takes in an integer n, and returns its square root. You are not allowed to use any built-in operations or functions to automatically find the square root.

Hint — build the answer using a string

def sqrt(n):
    # stuff

sqrt(0) # 0
sqrt(1) # 1.0
sqrt(2) # 1.414213562
sqrt(3) # 1.732050808
sqrt(4) # 2.0
sqrt(5) # 2.236067977

11) Letter pyramid

Write a function pyramid(string) that takes in a string string, and prints the following pattern.

pyramid('abcdef')

a
bc
def

If there are insufficient letters, add * characters to form a perfect triangle

pyramid('abcdefg')

a
bc
def
g***

pyramid('abcdefgh')

a
bc
def
gh**

pyramid('abcdefghijk')

a
bc
def
ghij
k****

12) Evaluating Math Expressions

You are given a string representing a math expression. For instance:

string = '1+2x3/4-5'

Without using built-in functions like eval or exec, write a function evaluate(string) that takes in a math expression string, solves it, and returns the result.

Assume that only addition, subtraction, multiplication and division operators will exist in the string
PEDMAS rule applies — multiplication/division before addition/subtraction

def evaluate(string):
    # stuff

evaluate('1+1')       # 2
evaluate('1+2x3')     # 7
evaluate('1-2x3+4x5') # 15

Conclusion

Let me know how long you took to solve them all!

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